Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	3^181378-2^(181378-1)	86540	Robert Price	01/2016
9752	24588^3305+3305^24588	86530	Hans Havermann	08/2020
9753	83^45080-2	86513	Lelio R Paula	08/2013
9754	(2^287367+2570)/2	86506	Stefano Morozzi	01/2020
9756	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
9755	(2^287360+1006)/2	86504	Stefano Morozzi	01/2020
9757	25*29^59147+20936	86498	Curtis Bright	05/2015
9758	2^287298+1871359	86486	Enzo Doria	05/2016
9759	118^41740-117	86481	Norbert Schneider	08/2018
9760	3*10^86478+89	86479	Robert Price	03/2017
9761	2^287272-79049	86478	Paul Bourdelais	02/2012
9762	(2^287259+2846)/2	86474	Stefano Morozzi	01/2020
9763	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
9764	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
9765	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
9766	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
9767	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
9768	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
9769	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
9770	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
9771	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
9772	(10^86453-1)/9	86453	Lew Baxter	10/2000
9773	(2^287172+658)/2	86448	Stefano Morozzi	01/2020
9774	(2^287146+2542)/2	86440	Stefano Morozzi	01/2020
9775	(2^287136+1726)/2	86437	Stefano Morozzi	01/2020
9776	(2^287128+958)/2	86434	Stefano Morozzi	01/2020
9777	87^44563-86^44563	86431	Robert Price	05/2015
9778	(26*10^86424-41)/3	86425	Robert Price	02/2022
9779	6^111057+61	86420	Lelio R Paula	12/2015
9780	2^287057-109909	86413	Enzo Doria	04/2014
9781	5^123608+22	86399	Lelio R Paula	10/2015
9782	10832^21411-21411^10832	86388	Norbert Schneider	01/2022
9783	(2^286970+618)/2	86387	Stefano Morozzi	01/2020
9784	(2^286916+2646)/2	86371	Stefano Morozzi	01/2020
9785	(2^286907+3690)/2	86368	Stefano Morozzi	01/2020
9786	(31*10^86364-121)/9	86365	Robert Price	06/2016
9787	(2^286868+2686)/2	86356	Stefano Morozzi	01/2020
9788	2^286859+71663	86354	Enzo Doria	04/2016
9789	(2^286845+1866)/2	86349	Stefano Morozzi	01/2020
9790	2^286740+29835	86318	Lelio R Paula	10/2013
9791	2*10^86310+9^86310	86311	Mike Oakes	05/2011
9792	11^82878-1860	86309	Enzo Doria	12/2012
9793	2223^25780+25780^2223	86285	Norbert Schneider	12/2019
9794	2^286547+16095	86260	Lelio R Paula	10/2013
9795	(58*10^86242+329)/9	86243	Robert Price	11/2017
9796	2^286455-110427	86232	Enzo Doria	05/2014
9797	(37*10^86230+53)/9	86231	Robert Price	05/2015
9798	8*3^180700+5	86217	Lelio R Paula	08/2014
9799	3^180697-40	86215	Lelio R Paula	12/2015
9800	(2^286383+3386)/2	86210	Stefano Morozzi	01/2020
9801	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
9802	(2^286295+1934)/2	86184	Stefano Morozzi	01/2020
9803	(157*10^86179-1)/3	86181	Robert Price	01/2022
9804	(2^286251+3974)/2	86170	Stefano Morozzi	01/2020
9805	2^286165+77	86145	Lelio R Paula	08/2012
9806	9*2^286140+7	86138	Lelio R Paula	08/2014
9807	(2^286128+1762)/2	86133	Stefano Morozzi	01/2020
9808	(118*10^86131+71)/9	86133	Robert Price	11/2021
9809	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
9810	(2^286077+1122)/2	86118	Stefano Morozzi	01/2020
9811	10^86110+161113	86111	Patrick De Geest	07/2013
9812	10^86110-69	86110	Robert Price	05/2011
9813	2^286036-869688105	86106	Lelio R Paula	07/2016
9814	(2^285946+2358)/2	86079	Stefano Morozzi	01/2020
9815	5*10^86076-21	86077	Robert Price	12/2021
9817	(77*10^86072+31)/9	86073	Robert Price	10/2015
9816	(2^285926+3382)/2	86073	Stefano Morozzi	01/2020
9818	2^285923+345	86072	Lelio R Paula	09/2013
9819	13^77266-90	86070	Lelio R Paula	11/2015
9820	2^285910-458903	86068	Enzo Doria	04/2015
9821	2^285904-125	86066	Lelio R Paula	08/2012
9822	(2^285882+2830)/2	86059	Stefano Morozzi	01/2020
9823	2^285836+65835	86046	Lelio R Paula	09/2013
9824	21587^9670+9670^21587	86034	Hans Havermann	08/2020
9825	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
9826	(2^285732+2682)/2	86014	Stefano Morozzi	01/2020
9827	(5*10^86011-107)/3	86012	Robert Price	01/2017
9828	6^110522+163	86003	Lelio R Paula	12/2015
9829	41^53323-40^53323	85999	Robert Price	07/2012
9830	2^285678-109617	85998	Enzo Doria	04/2014
9831	6^110506-16673	85991	Enzo Doria	02/2013
9832	2^285619-3001935	85980	Paul Bourdelais	04/2022
9833	2^285569-741	85965	Lelio R Paula	09/2013
9834	(32*10^85964+31)/9	85965	Robert Price	05/2015
9835	133^40466+132	85944	Norbert Schneider	02/2019
9836	23378^4743+4743^23378	85939	Hans Havermann	08/2020
9837	6*10^85910-7	85911	Dmitry Domanov	11/2010
9838	(412*10^85897-7)/9	85899	Robert Price	10/2017
9839	4*10^85881+63	85882	Robert Price	06/2016
9840	(2^285257+1514)/2	85871	Stefano Morozzi	01/2020
9841	(2^285248+3738)/2	85868	Stefano Morozzi	01/2020
9842	(10^85864+53)/9	85864	Robert Price	01/2015
9843	2^285230+345	85863	Lelio R Paula	09/2013
9844	21774^8777+8777^21774	85863	Hans Havermann	08/2020
9845	(5*10^85855-473)/9	85855	Robert Price	12/2017
9846	2^285199+75683	85854	Enzo Doria	04/2016
9847	(76*10^85847-211)/9	85848	Robert Price	10/2017
9848	p(17832)#/2+512	85845	Robert Price	05/2017
9849	(16*10^85839+167)/3	85840	Robert Price	10/2017
9850	11^82426-1230	85838	Enzo Doria	11/2012
9851	(14727^20593-1)/14726	85830	Serge Batalov	08/2020
9852	2^285113-109881	85828	Enzo Doria	04/2014
9853	(2^285033+1670)/2	85804	Stefano Morozzi	01/2020
9854	(2^285033+3854)/2	85804	Stefano Morozzi	01/2020
9855	(2^285035+3194)/2	85804	Stefano Morozzi	01/2020
9856	5^122746-92	85796	Lelio R Paula	10/2015
9857	2^285001-113461	85794	Enzo Doria	08/2014
9858	(11*10^85782-131)/3	85783	Robert Price	02/2017
9859	(2^284963+2778)/2	85783	Stefano Morozzi	01/2020
9860	(2^284960+3570)/2	85782	Stefano Morozzi	01/2020
9861	(2^284937+1706)/2	85775	Stefano Morozzi	01/2020
9863	2^284913-110491	85768	Enzo Doria	05/2014
9862	6^110220+47	85768	Lelio R Paula	12/2015
9864	(1966^26041-1)/1965	85765	Serge Batalov	08/2020
9865	20698^13909+13909^20698	85758	Hans Havermann	07/2020
9866	3*6^110202-5	85755	Lelio R Paula	10/2014
9867	9*10^85746+37	85747	Robert Price	12/2020
9868	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
9869	(3^179705+7)/250	85739	Lelio R Paula	12/2012
9870	(9127^21649-1)/9126	85734	Serge Batalov	08/2020
9871	2^284734-6555	85714	Lelio R Paula	09/2013
9872	(10^85712+53)/9	85712	Robert Price	01/2015
9873	3*10^85703+11	85704	Robert Price	11/2017
9874	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
9875	20728^13621+13621^20728	85694	Hans Havermann	07/2020
9876	22126^7459+7459^22126	85687	Hans Havermann	07/2020
9877	(9311^21589-1)/9310	85683	Serge Batalov	08/2020
9878	20^65855+83	85680	Lelio R Paula	01/2016
9879	6^110105+53	85679	Lelio R Paula	12/2015
9880	3*10^85672-73	85673	Robert Price	02/2021
9881	(10^85666-97)/3	85666	Robert Kinser	10/2017
9883	2^284567-7605	85664	Lelio R Paula	09/2013
9882	9*5^122555-2	85664	Lelio R Paula	10/2014
9884	5^122554-14	85662	Lelio R Paula	10/2015
9885	9*5^122543+4	85655	Lelio R Paula	10/2014
9886	(7*10^85647+173)/9	85647	Robert Price	01/2022
9888	3^179489-2^(179489-1)	85639	Robert Price	01/2016
9887	(2^284487+1970)/2	85639	Stefano Morozzi	01/2020
9889	(2^284477+1614)/2	85636	Stefano Morozzi	01/2020
9890	23693^4114+4114^23693	85633	Hans Havermann	07/2020
9891	19690^19941+19941^19690	85632	Norbert Schneider	03/2020
9892	2^284429+177	85622	Lelio R Paula	08/2012
9893	2*3^179452+5	85621	Lelio R Paula	07/2014
9894	21036^11711+11711^21036	85587	Hans Havermann	07/2020
9896	(19^66919+3^66919)/22	85572	Robert Price	07/2013
9895	(2^284265+602)/2	85572	Stefano Morozzi	01/2020
9897	66^47023-65	85561	Norbert Schneider	11/2014
9898	(2^284226+3802)/2	85561	Stefano Morozzi	01/2020
9899	(2^284228+2170)/2	85561	Stefano Morozzi	01/2020
9900	(56*10^85554+169)/9	85555	Robert Price	03/2022
9901	6^109943+13	85553	Lelio R Paula	12/2015
9902	2^284183-4747	85548	Yves Minet	05/2019
9903	(5637^22807-1)/5636	85547	Serge Batalov	08/2020
9904	20782^13071+13071^20782	85546	Hans Havermann	08/2020
9905	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
9906	(2^284136+2262)/2	85534	Stefano Morozzi	01/2020
9907	2^284133-3	85533	M. Frind & P. Underwood	07/2002
9908	2^284113+315	85527	Lelio R Paula	09/2013
9909	(2^284098+3082)/2	85522	Stefano Morozzi	01/2020
9910	(29*10^85517-23)/3	85518	Robert Price	03/2022
9911	(2^284070+1482)/2	85514	Stefano Morozzi	01/2020
9912	(2^284068+2866)/2	85513	Stefano Morozzi	01/2020
9913	(8721^21701-1)/8720	85511	Serge Batalov	08/2020
9914	22085^7438+7438^22085	85502	Hans Havermann	07/2020
9915	(28*10^85500+149)/3	85501	Robert Price	10/2017
9916	(16*10^85495-19)/3	85496	Robert Price	03/2016
9917	2^284004+177	85494	Lelio R Paula	08/2012
9918	(16*10^85473-91)/3	85474	Robert Price	06/2016
9919	66*10^85468+7	85470	Robert Price	07/2020
9920	3^179120+22	85462	Robert Price	12/2013
9921	2^283872-2792249	85454	Enzo Doria	03/2016
9922	(4703^23269-1)/4702	85449	Serge Batalov	08/2020
9923	(29*10^85438+259)/9	85439	Robert Price	04/2017
9924	2^283817+82875	85438	Lelio R Paula	09/2013
9925	(2^283815-5)/201	85435	Lelio R Paula	01/2013
9926	2^283796-125	85432	Lelio R Paula	08/2012
9927	(10174^21319-1)/10173	85432	Serge Batalov	08/2020
9928	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
9929	15^72592-28	85375	Lelio R Paula	11/2015
9930	2^283604-58695	85374	Lelio R Paula	09/2013
9931	21863^8034+8034^21863	85374	Hans Havermann	08/2020
9933	(44*10^85370-503)/9	85371	Robert Price	10/2017
9932	(2^283597+1854)/2	85371	Stefano Morozzi	01/2020
9934	496^31671+31671^496	85369	Norbert Schneider	07/2017
9935	(2^283578+478)/2	85366	Stefano Morozzi	01/2020
9936	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
9937	15^72572+92	85352	Lelio R Paula	11/2015
9938	6*10^85350-79	85351	Robert Price	03/2022
9939	2^283473-1615	85334	Lelio R Paula	09/2013
9940	(2^283469+2934)/2	85333	Stefano Morozzi	01/2020
9941	2^283466-15	85332	Lelio R Paula	08/2012
9942	(2^283437+3446)/2	85323	Stefano Morozzi	01/2020
9943	19966^18761+18761^19966	85320	Hans Havermann	07/2020
9944	(2^283411+3894)/2	85315	Stefano Morozzi	01/2020
9945	11^81916-7020	85307	Enzo Doria	02/2013
9946	6^109626-7	85306	Lelio R Paula	11/2014
9947	2^283374-110327	85305	Enzo Doria	05/2014
9948	33*10^85297+7	85299	Robert Price	07/2016
9949	(6010^22573-1)/6009	85297	Serge Batalov	08/2020
9950	1137^27908+27908^1137	85281	Norbert Schneider	04/2020
9951	18^67933+41	85275	Lelio R Paula	11/2015
9952	2^283271-109341	85274	Enzo Doria	04/2014
9953	(2^283266+3678)/2	85272	Stefano Morozzi	01/2020
9954	19688^19855-19855^19688	85262	Norbert Schneider	03/2020
9955	(2^283216+1926)/2	85257	Stefano Morozzi	01/2020
9956	(5*10^85254-191)/3	85255	Robert Price	05/2021
9957	(25*10^85249-73)/3	85250	Robert Price	09/2016
9958	2*5^121959+3	85246	Lelio R Paula	10/2014
9959	19834^19834+8947	85235	Henri Lifchitz	11/2004
9960	2^283140+1915	85234	Lelio R Paula	09/2013
9961	3*10^85227-97	85228	Robert Price	08/2017
9962	(16*10^85221-31)/3	85222	Robert Price	03/2016
9963	(2^283096+3186)/2	85221	Stefano Morozzi	01/2020
9964	2^283083+1869383	85217	Enzo Doria	05/2016
9965	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
9966	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
9967	2^283026-109893	85200	Enzo Doria	04/2014
9968	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
9969	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
9970	2^282860-109727	85150	Enzo Doria	04/2014
9971	(2^282847+13)/3	85145	Stefano Morozzi	03/2020
9972	(35*10^85141-611)/9	85142	Robert Price	02/2022
9973	2^282819+1869413	85138	Enzo Doria	05/2016
9974	3^178428+2	85132	Ray Chandler	07/2011
9975	19985^18162+18162^19985	85120	Hans Havermann	07/2020
9976	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
9977	(16^70687+5^70687)/21	85115	Robert Price	07/2013
9978	(2^282732+738)/2	85111	Stefano Morozzi	01/2020
9979	(2^282720+1590)/2	85107	Stefano Morozzi	01/2020
9980	(3^178352-2)/7	85095	Lelio R Paula	12/2012
9981	22150^6939+6939^22150	85085	Hans Havermann	07/2020
9982	11^81699-2790	85081	Enzo Doria	12/2012
9983	2^282612-95	85075	Lelio R Paula	08/2012
9984	2^282609-4069	85074	Yves Minet	02/2018
9985	75^45366-2	85065	Lelio R Paula	08/2013
9986	(2^282550+1918)/2	85056	Stefano Morozzi	01/2020
9987	(2^282515+3786)/2	85046	Stefano Morozzi	01/2020
9988	2^282511+69	85045	Lelio R Paula	08/2012
9989	69^46249+2	85045	Lelio R Paula	06/2013
9990	(2^282488+2382)/2	85038	Stefano Morozzi	01/2020
9991	(2^282489+1862)/2	85038	Stefano Morozzi	01/2020
9992	3^178226+10	85036	Robert Price	10/2013
9993	(2^282475+1050)/2	85034	Stefano Morozzi	01/2020
9994	(182*10^85017+43)/9	85019	Robert Price	11/2017
9995	(14*10^85010+73)/3	85011	Robert Price	04/2016
9996	9*2^282338-7	84994	Lelio R Paula	08/2014
9997	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
9998	5*10^84985-31	84986	Robert Price	12/2021
9999	20025^17504+17504^20025	84969	Hans Havermann	07/2020
10000	2^282203+5	84952	Lelio R Paula	08/2012

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Probable Primes Top 10000

(290751 PRPs in the top)